A POCS-based graph matching algorithm

A novel projections onto convex sets (POCS) graph matching algorithm is presented. Two-way assignment constraints are enforced without using elaborate penalty terms, graduated nonconvexity, or sophisticated annealing mechanisms to escape from poor local minima. Results indicate that the presented algorithm is robust and compares favorably to other well-known algorithms.     

A graduated assignment algorithm for graph matching

A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated nonconvexity, two-way (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational complexity [O(lm), where l and m are the number of links in the two graphs] and robustness in the presence of noise offer advantages over traditional combinatorial approaches. The algorithm, not restricted to any special class of graph, is applied to subgraph isomorphism, weighted graph matching, and attributed relational graph matching. To illustrate the performance of the algorithm, attributed relational graphs derived from objects are matched. Then, results from twenty-five thousand experiments conducted on 100 mode random graphs of varying types (graphs with only zero-one links, weighted graphs, and graphs with node attributes and multiple link types) are reported. No comparable results have been reported by any other graph matching algorithm before in the research literature. Twenty-five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated     

A parallel algorithm for graph matching and its MasParimplementation

Search of discrete spaces is important in combinatorial optimization. Such problems arise in artificial intelligence, computer vision, operations research, and other areas. For realistic problems, the search spaces to be processed are usually huge, necessitating long computation times, pruning heuristics, or massively parallel processing. We present an algorithm that reduces the computation time for graph matching by employing both branch-and-bound pruning of the search tree and massively-parallel search of the as-yet-unpruned portions of the space. Most research on parallel search has assumed that a multiple-instruction-stream/multiple-data-stream (MIMD) parallel computer is available. Since massively parallel stream (SIMD) computers are much less expensive than MIMD systems with equal numbers of processors, the question arises as to whether SIMD systems can efficiently handle state-space search problems. We demonstrate that the answer is yes, and in particular, that graph matching has a natural and efficient implementation on SIMD machines     

一种基于图割理论的快速立体匹配算法

针对传统的立体匹配算法中存在的低纹理区域和遮挡区域匹配精度低、实时性不好等问题,提出了一种基于图割理论的立体匹配算法.把图像分割成色彩单一的不同区域;计算初始视差图,利用可靠点求取各分割区域的平面模板参数,对模板参数相同的相邻区域进行融合;构造全局能量函数,采用图割算法求取全局能量最小的视差最优分配.实验结果表明,该算法对低纹理区域和遮挡区域均有较好的匹配结果,能够满足高精度、高实时性的要求.     

A (sub)graph isomorphism algorithm for matching large graphs

We present an algorithm for graph isomorphism and subgraph isomorphism suited for dealing with large graphs. A first version of the algorithm has been presented in a previous paper, where we examined its performance for the isomorphism of small and medium size graphs. The algorithm is improved here to reduce its spatial complexity and to achieve a better performance on large graphs; its features are analyzed in detail with special reference to time and memory requirements. The results of a testing performed on a publicly available database of synthetically generated graphs and on graphs relative to a real application dealing with technical drawings are presented, confirming the effectiveness of the approach, especially when working with large graphs.     

一种改进的基于图割的立体匹配算法

为了提高立体匹配算法的精确度,提出了一种结合图割与Mean Shift图像分割的立体匹配算法。首先用Mean Shift算法对参考图像进行图像分割,得到分割后的标记图,然后将分割信息结合到图割算法的能量函数中,最后用改进的能量函数和图割算法得出致密的视差图。实验结果表明,提出的算法具有更高的精确度和更好的边缘特征。     

A genetic algorithm and its parallelization for graph matching with similarity measures

Graph matching and similarity measures of graphs have many applications to pattern recognition, machine vision in robotics, and similarity-based approximate reasoning in artificial intelligence. This paper proposes a method of matching and a similarity measure between two directed labeled graphs. We define the degree of similarity, the similar correspondence, and the similarity map which denotes the matching between the graphs. As an approximate computing method, we apply genetic algorithms (GA) to find a similarity map and compute the degree of similarity between graphs. For speed, we make parallel implementations in almost all steps of the GA. We have implemented the sequential GA and the parallel GA in C programs, and made simulations for both GAs. The simulation results show that our method is efficient and useful. This work was presented, in part, at the Second International Symposium on Artificial Life and Robotics, Oita Japan, February 18–20, 1997     

图谱和Kuhn-Munkres算法在图匹配中的应用研究

为了对图数据库中的结构化数据进行有效的匹配分析,提出了基于全局结构相似度以及节点位置相似度的Kuhn-Munkres算法。首先对图数据构建全局以及节点位置矩阵,全局相似度矩阵用邻接矩阵的拉普拉斯谱特征构造,位置相似度矩阵首先使用高斯核函数进行节点相对位置的归一化计算,再利用其谱特征构造。节点位置相似度主要描述图所有节点之间的相对位置,弥补了全局结构相似度只刻画图整体结构的不足。最后使用Kuhn-Munkres算法进行图匹配,得到二分图的最大权匹配。实验表明,改进的Kuhn-Munkres算法有效提高了节点之间的匹配正确率。     

Structural graph matching using the EM algorithm and singular valuedecomposition

This paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions: 1) commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximum-likelihood estimation using the apparatus of the EM algorithm; and 2) we cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows one to efficiently recover correspondence matches using the singular value decomposition. We experiment with the method on both real-world and synthetic data. Here, we demonstrate that the method offers comparable performance to more computationally demanding methods     

A new graph matching method for point-set correspondence using the EM algorithm and Softassign

Finding correspondences between two point-sets is a common step in many vision applications (e.g., image matching or shape retrieval). We present a graph matching method to solve the point-set correspondence problem, which is posed as one of mixture modelling. Our mixture model encompasses a model of structural coherence and a model of affine-invariant geometrical errors. Instead of absolute positions, the geometrical positions are represented as relative positions of the points with respect to each other. We derive the Expectation–Maximization algorithm for our mixture model. In this way, the graph matching problem is approximated, in a principled way, as a succession of assignment problems which are solved using Softassign. Unlike other approaches, we use a true continuous underlying correspondence variable. We develop effective mechanisms to detect outliers. This is a useful technique for improving results in the presence of clutter. We evaluate the ability of our method to locate proper matches as well as to recognize object categories in a series of registration and recognition experiments. Our method compares favourably to other graph matching methods as well as to point-set registration methods and outlier rejectors.     

The discriminant elastic graph matching algorithm applied to frontal face verification

In this paper a generalized framework for face verification is proposed employing discriminant techniques in all phases of elastic graph matching. The proposed algorithm is called discriminant elastic graph matching (DEGM) algorithm. In the first step of the proposed method, DEGM, discriminant techniques at the node feature vectors are used for feature selection. In the sequel, the two local similarity values, i.e., the similarity measure for the projected node feature vector and the node deformation, are combined in a discriminant manner in order to form the new local similarity measure. Moreover, the new local similarity values at the nodes of the elastic graph are weighted by coefficients that are derived as well from discriminant analysis in order to form a total similarity measure between faces. The proposed method exploits the individuality of the human face and the discriminant information of elastic graph matching in order to improve the verification performance of elastic graph matching. We have applied the proposed scheme to a modified morphological elastic graph matching algorithm. All experiments have been conducted in the XM2VTS database resulting in very low error rates for the test sets.     

A Lagrangian relaxation network for graph matching

A Lagrangian relaxation network for graph matching is presented. The problem is formulated as follows: given graphs G and g, find a permutation matrix M that brings the two sets of vertices into correspondence. Permutation matrix constraints are formulated in the framework of deterministic annealing. Our approach is in the same spirit as a Lagrangian decomposition approach in that the row and column constraints are satisfied separately with a Lagrange multiplier used to equate the two "solutions". Due to the unavoidable symmetries in graph isomorphism (resulting in multiple global minima), we add a symmetry-breaking self-amplification term in order to obtain a permutation matrix. With the application of a fixpoint preserving algebraic transformation to both the distance measure and self-amplification terms, we obtain a Lagrangian relaxation network. The network performs minimization with respect to the Lagrange parameters and maximization with respect to the permutation matrix variables. Simulation results are shown on 100 node random graphs and for a wide range of connectivities.     

A generative model for graph matching and embedding

This paper shows how to construct a generative model for graph structure through the embedding of the nodes of the graph in a vector space. We commence from a sample of graphs where the correspondences between nodes are unknown ab initio. We also work with graphs where there may be structural differences present, i.e. variations in the number of nodes in each graph and their edge structure. We characterise the graphs using the heat-kernel, and this is obtained by exponentiating the Laplacian eigensystem with time. The idea underpinning the method is to embed the nodes of the graphs into a vector space by performing a Young-Householder decomposition of the heat-kernel into an inner product of node co-ordinate matrices. The co-ordinates of the nodes are determined by the eigenvalues and eigenvectors of the Laplacian matrix, together with a time-parameter which can be used to scale the embedding. Node correspondences are located by applying Scott and Longuet-Higgins algorithm to the embedded nodes. We capture variations in graph structure using the covariance matrix for corresponding embedded point positions. We construct a point-distribution model for the embedded node positions using the eigenvalues and eigenvectors of the covariance matrix. We show how to use this model to both project individual graphs into the eigenspace of the point position covariance matrix and how to fit the model to potentially noisy graphs to reconstruct the Laplacian matrix. We illustrate the utility of the resulting method for shape analysis using data from the Caltech–Oxford and COIL databases.     

A dynamical systems approach to weighted graph matching

Graph matching is a fundamental problem that arises frequently in the areas of distributed control, computer vision, and facility allocation. In this paper, we consider the optimal graph matching problem for weighted graphs, which is computationally challenging due the combinatorial nature of the set of permutations. Contrary to optimization-based relaxations to this problem, in this paper we develop a novel relaxation by constructing dynamical systems on the manifold of orthogonal matrices. In particular, since permutation matrices are orthogonal matrices with nonnegative elements, we define two gradient flows in the space of orthogonal matrices. The first minimizes the cost of weighted graph matching over orthogonal matrices, whereas the second minimizes the distance of an orthogonal matrix from the finite set of all permutations. The combination of the two dynamical systems converges to a permutation matrix, which provides a suboptimal solution to the weighted graph matching problem. Finally, our approach is shown to be promising by illustrating it on nontrivial problems.     

A people-to-people matching system using graph mining techniques

A people-to-people matching system (or a match-making system) refers to a system in which users join with the objective of meeting other users with the common need. Some real-world examples of these systems are employer-employee (in job search networks), mentor-student (in university social networks), consume-to-consumer (in marketplaces) and male-female (in an online dating network). The network underlying in these systems consists of two groups of users, and the relationships between users need to be captured for developing an efficient match-making system. Most of the existing studies utilize information either about each of the users in isolation or their interaction separately, and develop recommender systems using the one form of information only. It is imperative to understand the linkages among the users in the network and use them in developing a match-making system. This study utilizes several social network analysis methods such as graph theory, small world phenomenon, centrality analysis, density analysis to gain insight into the entities and their relationships present in this network. This paper also proposes a new type of graph called “attributed bipartite graph”. By using these analyses and the proposed type of graph, an efficient hybrid recommender system is developed which generates recommendation for new users as well as shows improvement in accuracy over the baseline methods.     

一种基于混合匹配的指纹识别方法

为克服传统的基于细节点匹配的不足,对基于点模式匹配算法与改进的2DPCA匹配算法的混合识别算法进行了改进。改进后的算法在点模式匹配算法中加入改进的2DPCA算法的初匹配得分权重,提高了点模式匹配算法的准确性;并利用点模式匹配算法对2DPCA算法的匹配结果进行二次匹配,同时也提高了2DPCA算法匹配的准确率。     

A simple contour matching algorithm

Two similarity measures between strings are proposed. This correspondence also describes an experiment performed to illustrate the inadequacy of a commonly used measure.